I have strangely never bothered to pay much attention to the topic of "kazoku" in Japanese. There are so many words for family members, that I need help sorting them out. I realize there's a difference in the words used to address one's own mother and addressing another person's mother, etc, but I don't know which is which. Please help me figure it all out here.

Well, maybe I/we am/are not quite sure what you are referring to specifically. Mom is mom and mother is mother. Your mom is your mom and my mother is my mother even in Japanese, basically. I don’t know if you use “mater” or “old cheese” when you want to address your matriarch, though.

It’s kind of tough to generalize the usage.What did you address your mother when you were a baby? Ma? Mummy? Do you use the word to your boss in your office? Like “How is your mummy, boss?” Or, do you use the word to your close friend in the casual conversation? How about among your brothers?Thus, the “appropriate term” is not decided by grammar but according to the social relationship.For instance, the word okaasan(お母さん) is considered a relatively casual term. It’s like something between mother and mom. I mean, it would be natural to mention your friend’s mom saying きみのお母さん. We don’t have any specific rules for that. It's just a matter of politeness and your personal preference, so to speak.Another example is what you wrote above. Kazoku vs gokazoku. The only rule here is that gokazoku is more polite. That’s all. You can use kazoku for another’s family as well.ママ母さんお母さんお母様母母親母上All the words above can be used in any situation if you want to as a translation of the word “mother”. But I have no idea which one is “the best to use”. It depends.